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Vlad [161]
3 years ago
6

Evaluate the given integral by changing to polar coordinates. sin(x2 + y2) dA R , where R is the region in the first quadrant be

tween the circles with center the origin and radii 2 and 3
Mathematics
1 answer:
koban [17]3 years ago
8 0

Set

\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dA=r\,\mathrm dr\,\mathrm d\theta

The region R is given in polar coordinates by the set

R=\left\{(r,\theta)\mid2\le r\le3,0\le\theta\le\dfrac\pi2\right\}

So we have

\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_2^3r\sin(r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac\pi4(\cos4-\cos9)}

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Answer:

\huge\boxed{x=3}

Step-by-step explanation:

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7 0
3 years ago
A.) 15.7in<br> B.) 31.4in<br> C.) 40in<br> D.) 62.8in
IrinaK [193]

Answer:

31.4 in

Step-by-step explanation:

This is a tricky question,

if you observe the shape carefully, you will notice that if you mirror (flip outward) each curve surface of each quardrant, what you will end up with is a complete circle with a radius of 5 inches.

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4 0
2 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=2%20%20%5Ctimes%202%20" id="TexFormula1" title="2 \times 2 " alt="2 \times 2 " align="absmid
ICE Princess25 [194]

The answer is 4

hope this helps

8 0
3 years ago
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Carlos had $65.00 in his checking account. By mistake he wrote out a check for $82.00. By how much is his checking account overd
mylen [45]
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His account is overdrawn by $17.
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2 years ago
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ehidna [41]

Answer:

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Step-by-step explanation:

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